Various types of cooling mechanisms can be used to remove waste heat from high power semiconductor devices such as power FETs and IGBTs. In cases where the waste heat and/or the ambient temperature are very high, the power device packages can be mounted on a liquid-cooled heat exchanger or a cold plate through which liquid coolant is circulated. The heat transfer can be significantly improved by bringing the liquid coolant directly into contact with the semiconductor chip (die), as shown in the Patent Application Publication Nos. 2006/0022334; 2006/0034052; 2006/0291164; and 2007/0063337, all assigned to Delphi Technologies, Inc. As described in these patent documents, a major surface of the semiconductor chip (say, the drain terminal of a power FET) can be undercut to define an array of fluid conducting channels through the bulk region of the chip, and the chip can be packaged so that some or all of the circulating fluid flows through the channels to remove heat from the chip. As described in the aforementioned Publication No. 2006/0022334, for example, the direct die cooling approach can be implemented on a modular or stand-alone basis by packaging a channelled semiconductor chip in a liquid cooled container, and mounting the container on a circuit board with both electrical and fluid interconnects.